Ideas in Geometry/Constructions II
4.2 Trickier Constructions
This lesson focuses on constructing triangles. please note that some of the videos use a protractor to measure angles, we are using a compass to copy the angles.
We focus on four main constructions for triangles. This section gives us different constructions to make tirangles when given different parts of the triangle These constructions are done when you are given three different pieces of information. They can be completed using a compass and straight edge.
Side Angle Side (SAS Triangle)
This construction should be used when you are given a side, an angle adjacent to that side, and a side adjacent to that angle. Its like an angle sandwich! 1. Transfer one side that that it starts at the vertex of the angle 2. Transfter the other side so that it starts at the vertex 3. Connect the end points of all moved line segments
SIde Side Side - you are given all three sides of the triangle, and no angles.
1. choose a side and select one of its endpoints 2. Draw a circle of radius equal to the length of the seond side aorund the choses end point 3. draw a circle of radius equal o the length of the third side around the other end point 4. connect the end pointd of the first side and the interection of the circles. This is the desired triangle
here is an example of how to do this side side side video
Side Angle Angle
1. start with given side and place adjacent angle at one of its end points 2. move second angle so that it shares a leg with the leg of the first angle- not the leg with the side 3. extend the side past the first angle, forming a new angle with the leg of the second angle 4. move this new angle to the other end point of the slide, extending the legs of this angle and the first angle will produce the desired triangle you are given a side, the angle adjacent, and the angle
here is an example video SAA
Angle Side Side is a construction to be careful of. it can produce more than one triangle, therefore making it an unreliable construction.